Luis Evaristo Caraballo

The block-sharing strategy for area monitoring missions using a decentralized multi-UAV system

In monitoring missions, using a cooperative team of Unmanned Aerial Vehicles (UAVs), the goal is to minimize the elapsed time between two consecutive observations of any point in the area. Techniques based in area partitioning achieve the goal when the sub-area assigned to each UAV is according to its capabilities. In previous work of the authors [1] it was presented the one-to-one strategy to obtain in a decentralized way a near optimal partition from any initial grid partition. In this paper a generalization of that strategy called the block-sharing technique is presented. The goal in this work is to accelerate the convergence to an optimal partition with respect to previous work.

The block-information-sharing strategy for task allocation: A case study for structure assembly with aerial robots ☆

A new paradigm for task allocation in cooperative multi-robot systems is proposed in this paper. The block-information-sharing (BIS) strategy is a fully distributed approach, where robots dynamically allocate their tasks following the principle of share & divide to maintain an optimal allocation according to their capabilities. Prior studies on multi-robot information sharing strategies do not formally address the proof of convergence to the optimal allocation, nor its robustness to dynamic changes in the execution of the global task. The BIS strategy is introduced in a general framework and the convergence to the optimal allocation is theoretically proved. As an illustration of the approach, the strategy is applied to the automatic construction of truss structures with aerial robots. In order to demonstrate the benefits of the strategy, algorithms and simulations are presented for a team of heterogeneous robots that can dynamically reallocate tasks during the execution of a mission.

A General Framework for Synchronizing a Team of Robots Under Communication Constraints

This paper addresses a synchronization problem that arises when a team of robots needs to communicate while repeatedly performing assigned tasks in a cooperative scenario. Each robot has a limited communication range and moves along a previously defined closed trajectory. When two robots are close enough, a communication link may be established, allowing the robots to exchange information. The goal is to schedule the motions such that the entire system can be synchronized for maximum information exchange; that is, every pair of neighbors always visit the feasible communication link at the same time. An algorithm for scheduling the team of robots in this scenario is proposed and a robust framework that assures the synchronization of a large team of robots is presented. Simulations, experiments, and computational results demonstrate the applicability of the algorithm. The approach allows the design of fault-tolerant systems that can be used for multiple tasks, such as surveillance, area exploration, and searching for targets in hazardous environments, among others.

Maximum Box Problem on Stochastic Points

Given a finite set of weighted points in \(\mathbb {R}^d\) (where there can be negative weights), the maximum box problem asks for an axis-aligned rectangle (i.e., box) such that the sum of the weights of the points that it contains is maximized. We consider that each point of the input has a probability of being present in the final random point set, and these events are mutually independent; then, the total weight of a maximum box is a random variable. We aim to compute both the probability that this variable is at least a given parameter, and its expectation. We show that even in \(d=1\) these computations are #P-hard, and give pseudo polynomial-time algorithms in the case where the weights are integers in a bounded interval. For \(d=2\), we consider that each point is colored red or blue, where red points have weight \(+1\) and blue points weight \(-\infty \). The random variable is the maximum number of red points that can be covered with a box not containing any blue point. We prove that the above two computations are also #P-hard, and give a polynomial-time algorithm for computing the probability that there is a box containing exactly two red points, no blue point, and a given point of the plane.

Computing the k-resilience of a synchronized multi-robot system

We study an optimization problem that arises in the design of covering strategies for multi-robot systems. Consider a team of n cooperating robots traveling along predetermined closed and disjoint trajectories. Each robot needs to periodically communicate information to nearby robots. At places where two trajectories are within range of each other, a communication link is established, allowing two robots to exchange information, provided they are “synchronized”, i.e., they visit the link at the same time. In this setting a communication graph is defined and a system of robots is called synchronized if every pair of neighbors is synchronized. If one or more robots leave the system, then some trajectories are left unattended. To handle such cases in a synchronized system, when a live robot arrives to a communication link and detects the absence of the neighbor, it shifts to the neighboring trajectory to assume the unattended task. If enough robots leave, it may occur that a live robot enters a state of starvation, failing to permanently meet other robots during flight. To measure the tolerance of the system under this phenomenon we define the k-resilience as the minimum number of robots whose removal may cause k surviving robots to enter a state of starvation. We show that the problem of computing the k-resilience is NP-hard if k is part of the input, even if the communication graph is a tree. We propose algorithms to compute the k-resilience for constant values of k in general communication graphs and show more efficient algorithms for systems whose communication graph is a tree.

Efficient Inspection of Underground Galleries Using k Robots with Limited Energy

We study the problem of optimally inspecting an underground (underwater) gallery with k agents. We consider a gallery with a single opening and with a tree topology rooted at the opening. Due to the small diameter of the pipes (caves), the agents are small robots with limited autonomy and there is a supply station at the gallery’s opening. Therefore, they are initially placed at the root and periodically need to return to the supply station. Our goal is to design off-line strategies to efficiently cover the tree with k small robots. We consider two objective functions: the covering time (maximum collective time) and the covering distance (total traveled distance). The maximum collective time is the maximum time spent by a robot needs to finish its assigned task (assuming that all the robots start at the same time); the total traveled distance is the sum of the lengths of all the covering walks. Since the problems are intractable for big trees, we propose approximation algorithms. Both efficiency and accuracy of the suboptimal solutions are empirically showed for random trees through intensive numerical experiments.

Asymmetric polygons with maximum area

We say that a polygon inscribed in the circle is asymmetric if it contains no two antipodal points being the endpoints of a diameter. Given

Finding Unknown Nodes in Phylogenetic Graphs

n

Matching colored points with rectangles

diameters of a circle and a positive integer

Extremal antipodal polygons and polytopes

k<n